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%I #4 Jan 15 2014 07:32:17
%S 81,576,576,3992,9710,3992,26088,160075,160075,26088,167892,2423417,
%T 6175786,2423417,167892,1060410,36199157,216691834,216691834,36199157,
%U 1060410,6648825,523547651,7433913626,17653658980,7433913626,523547651
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with the sum of each 2X2 subblock maximum and minimum lexicographically nondecreasing columnwise and nonincreasing rowwise
%C Table starts
%C .......81..........576............3992..............26088..............167892
%C ......576.........9710..........160075............2423417............36199157
%C .....3992.......160075.........6175786..........216691834..........7433913626
%C ....26088......2423417.......216691834........17653658980.......1402427258099
%C ...167892.....36199157......7433913626......1402427258099.....257369376150524
%C ..1060410....523547651....244518790287....106304515215910...45081614802280999
%C ..6648825...7519969703...7937748092921...7914658615624380.7733449708119520219
%C .41411637.106697433668.252930693591705.575146083513956152
%H R. H. Hardin, <a href="/A235742/b235742.txt">Table of n, a(n) for n = 1..71</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 12]
%F k=2: [order 78]
%e Some solutions for n=2 k=4
%e ..1..0..0..2..2....1..0..2..1..2....1..0..0..1..2....2..0..2..1..2
%e ..0..0..1..0..1....0..0..1..2..2....0..0..1..2..2....0..0..2..1..1
%e ..0..0..0..2..0....0..0..1..2..2....0..0..2..2..2....1..1..0..1..2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 15 2014
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